Solvability of Sequential Fractional Differential Equation at Resonance

Salem, Ahmed; Almaghamsi, Lamya

doi:10.3390/math11041044

Cited by 6 publications

(1 citation statement)

References 36 publications

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“…In the theory of coincidence degree, the construction of relevant operators is highly skilled, which brings difficulties to the application of this method. Consequently, there are relatively few works [69][70][71][72][73] on the existence of solutions to fractional differential equations via coincidence degree theory.…”

Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

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The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings.

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